名校
解题方法
1 . 已知函数
在
上为奇函数,
,
.
(1)求实数
的值;
(2)指出函数
的单调性(说明理由,不需要证明);
(3)设对任意
,都有
成立;请问是否存在
的值,使
最小值为
,若存在求出
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8932f7d6ef4d9e276fdfd582d9fd9934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)指出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)设对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1fd4b6d54199a7ef857ecd2359c0f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb1359b9d7aac57284a7886ab2a7b1b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/459c84c9addfbd1cdd0a877ba7c584e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2022-09-29更新
|
804次组卷
|
3卷引用:第5章 三角函数(基础、典型、易错、压轴)分类专项训练(2)
(已下线)第5章 三角函数(基础、典型、易错、压轴)分类专项训练(2)浙江省杭州第四中学吴山校区2021-2022学年高一上学期期末数学试题福建省龙岩市长汀县第一中学分校2023-2024学年高一上学期第三次月考数学试题
解题方法
2 . 已知函数
.
(1)若
,记函数
.当
时,写出
的增区间.(不需要证明);
(2)记函数
.若
在区间
上最大值是2,求
的值;
(3)记函数
,对
,有
成立,求实数
取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1499d8d9850e52e16cf2b193324d66.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db0e7e85ec248ff7572bf76e90967ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
(2)记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73ca87a96058c70a8e4fb187a8bfe3e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab409bb25958c2f01c73e26042c6f51e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cfe951c0b4ddd9d007a147bef01a0c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd80964c195b96b377026eade71f3d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
解题方法
3 . 对于定义在R上的函数
,若存在正数m与集合A,使得对任意的
,当
,且
时,都有
,则称函数
具有性质
.
(1)若
,判断
是否具有性质
,并说明理由;
(2)若
,且
具有性质
,求m的最大值;
(3)若函数
的图像是连续曲线,且当集合
(a为正常数)时,
具有性质
,证明:
是R上的单调函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d200a7afe1e011713e14886a6887e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11b5a67de6c52bc02b4c2a5fdee81234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/040c65383c37f33033de5d9760cf8d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e7d767aea324236dfb52dc4618979bd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8327be2dd861aba12773e281c6f3582.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1452b4b627eb5259704a7eb3ffa3113.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b923078510697d5f7f9ea392eb76dd9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23e59905a17fbf584249c3d1f6ebf576.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d4e6d66cb4062c3949923959f04dbb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2501a1216ce5aa644aa139a0fc99678f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
名校
解题方法
4 . 已知函数
,
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c85467b0027305f2d3757b0ba5bf8b.png)
(1)若
,且
,试比较
与
的大小关系,并说明理由;
(2)若
,且
,证明:
(i)
;
(ii)
.
(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1060c34e676f9e4048f396023fa6a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b87dad80ff155f615b17fbe8bf4db00a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c85467b0027305f2d3757b0ba5bf8b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/477401fbd54f365121b648e4d8fcf38b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f13c49cbcdca5ed2e81d229819357b9.png)
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc6ecd08de6b156b5fa2bda453c855f3.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe64030d6e08f7607b7e3d9a724a79c9.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9e0f63cd71701bdf260b1510c72ee8f.png)
您最近一年使用:0次
名校
解题方法
5 . 已知函数
的定义域是D,若对于任意的
,
,当
时,都有
,则称函数
在D上为不减函数.现有定义在
上的函数
满足下述条件:
①对于
,总有
,且
,
;
②对于
,若
,则
.
试证明下列结论:
(1)对于
,若
,则
;
(2)a)
在
上为不减函数;
b)对
,都有
;
(3)当
时,有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28e384ba050b238e11f7c74d3002aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c61c8d37c767ba727cc7f5f7e00a7d96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790daaa89fc9d093f45023becf765697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbb7af9e416682c9be1ff154ec3fbfdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81ed7f6a4475e0fa682fa81ee747da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e27c24244b1fdbf1455087c2ebf41c8b.png)
②对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0232209f5de09f72b997e0099b9de5f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7563ceaa2d4ae02f31d47b53708edc75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff755b55a86b26a7f3e7def591b5b315.png)
试证明下列结论:
(1)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3367bd41ff428d7a608511cfb1f3cb11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aa468658500142da664ca688d4d4d4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d096dd04098cafabf4211054353feec8.png)
(2)a)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
b)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e511095b9802e0e54c3bcac8be160e58.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef6101294ff728fdef676a5786590908.png)
您最近一年使用:0次
名校
解题方法
6 . 定义
为双曲正弦函数,
为双曲余弦函数,它们是一类与三角函数类似的函数.
(1)试判断双曲正弦函数
的单调性,并用定义证明;
(2)①类比同角三角函数的平方关系,试写出
与
的关系式,并给予证明;
②对
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e183cfec7ad0c15ba454415017e3ec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3442020c24433f0e30b455d3e2bd0e3.png)
(1)试判断双曲正弦函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ae841e173b7700db59a369202dcbcf.png)
(2)①类比同角三角函数的平方关系,试写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ae841e173b7700db59a369202dcbcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c499a131f534409ee96f17e1d9f44b9e.png)
②对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c08d4d681c6e84e695b2a467dde8f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77474ddd5262fcbf0877981ce802adb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2022-03-17更新
|
473次组卷
|
2卷引用:专题03E函数解答题
名校
解题方法
7 . 已知函数
,
,其中
.
(1)
时,判断函数
的单调性(不需证明),并解不等式
;
(2)定义
上的函数
如下:
,若
在
上是减函数,当实数m取最大值时,求t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb0e3b7384e7f0a324862c6589026b62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d0ea0821f8bb3cfbeab0bc5dab8c572.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ae8d3e61598b3f81d3bd8a337c9801.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a51944c720568f35d443589dfc1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d87d0e14d115dd37aa69f34602d3d4.png)
(2)定义
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fa6a39515ef32c355c1a35be2da988c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e1ef4b55075ea0b421bae124a09614.png)
您最近一年使用:0次
2022-02-07更新
|
928次组卷
|
2卷引用:第4章 指数概念与对数函数(基础、典型、易错、新文化、压轴)专项训练-2022-2023学年高一数学考试满分全攻略(人教A版2019必修第一册)
名校
解题方法
8 . 已知
,函数
.
(1)若
有两个零点
,且
的最小值为
,当
时,判断函数
在
上的单调性,并说明理由;
(2)设
,记
为集合
中元素的最大者与最小者之差.若对
,
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331d5e308cd5469e0f28a8d75f79903f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b3f51410d969f9fb41a595a028a6f06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0268e85df43d66b031e0eccb11284452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f88a76f947e7022ef0c5efd6db060c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee3c6cdb19ac03dc3c28cd63b09dc907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4802dfb4352b1162b6cda12fa469f91e.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebc20d351d51723c9b0a07a20ac14114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0225bca34eaf19544939b29153aac1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0e3589ab6dda85eb6dc9cab30878f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff5474708041244835175778925a7ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8119e4e1c474bc2adbe014628043609.png)
您最近一年使用:0次
2022-01-23更新
|
376次组卷
|
3卷引用:重难点03函数(15种解题模型与方法)(4)
(已下线)重难点03函数(15种解题模型与方法)(4)山东省淄博市2021-2022学年高一上学期期末数学试题广东省东莞市东华高级中学、东华松山湖高级中学2023-2024学年高一上学期12月月考数学试题
解题方法
9 . 若函数
满足
,则称函数
为“倒函数”.
(1)判断函数
和
是否为倒函数,并说明理由;
(2)若
(
恒为正数),其中
是偶函数,
是奇函数,求证:
是倒函数;
(3)若
为倒函数,求实数m、n的值;判定函数
的单调性,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdfaa3716ef9b13f4bdfe0b234df9932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4508929da7db1adb7cc7a70e91be543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc9f0517304e39719c81d724ce2b860.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c118383937a12c505289f31b5d70a3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde66f0ef8ea3ac6d6ac91a93ba69ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde66f0ef8ea3ac6d6ac91a93ba69ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b2373399a8dcbcfaa270d31e5e7bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4211dfe3924d94e4b99f525e43a31cc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
您最近一年使用:0次
2022·上海·模拟预测
10 . 已知函数
,甲变化:
;乙变化:
,
.
(1)若
,
,
经甲变化得到
,求方程
的解;
(2)若
,
经乙变化得到
,求不等式
的解集;
(3)若
在
上单调递增,将
先进行甲变化得到
,再将
进行乙变化得到
;将
先进行乙变化得到
,再将
进行甲变化得到
,若对任意
,总存在
成立,求证:
在R上单调递增.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e746284f8292034744ef19606f34ba0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7da1ccb2c68857801d3684316685994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a51944c720568f35d443589dfc1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee6881a170f6ef9ed5c133b95c2f448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697a2a61d367fe01830b6b5995a2c38d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318a16f1950d06e5500c76d8f81a507f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b3deb8eb89eb6be966c64d81acb292b.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9414348d57c7fc77dcfa8f0744cb0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a4df880ff8c0322708ca3048aa665c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a4df880ff8c0322708ca3048aa665c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef23cf7d8c1b7e52a15e052768cd055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/733b1f3ace6bd767fe4a26dc8098b8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/733b1f3ace6bd767fe4a26dc8098b8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf729dc97c117b83cfa0769e02e3ce1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60e15191afd613e5d8215bfa73ac86ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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